Quiz04 Div3 Soln
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ME 274 – Spring 2009 Quiz No. 4 – Div 3 Monday, February 9
SOLUTION
The mechanism shown below is made up of links OA and BC. Links OA and BC are pinned to ground at points O and C, respectively. Pin A of link OA is able to slide within a slot that is cut in link BC, as shown. Pins O and C are on the same horizontal line. At the instant shown, • link BC is vertical with L = 400 mm. • link OA is rotating in the CW sense at a rate of ωBC = 8 rad/sec.
y B
At the instant shown, find: a) the angular velocity of link BC. Write your answer as a vector.
A
b) the value for L! . HINT: In relating the velocities of A and C, use an observer attached to link BC. Also, let the xyz axes be attached to link BC.
500 mm
L
Link OA:
ωOA
v A = vO + ! OA "!r A/O
(
= 0 + (! OA k ) "! 0.3i + 0.4 j
)
x
= #0.4 ! OA i + 0.3! OA j Also,
O
v A = vC + ( v A/C )rel + ! "!r A/C
(
= 0 + L! j + (! BC k ) "! 0.4 j
)
= #0.4 ! BC i + L! j Equating and balancing coefficients:
! 0.4 " OA = !0.4 " BC j : 0.3" OA = L!
i:
# #
" BC = ( !8 k ) rad / sec L! = ( 0.3) ( !8 ) = !2.4 m / sec
C
SOLUTION
The mechanism shown below is made up of links OA and BC. Links OA and BC are pinned to ground at points O and C, respectively. Pin A of link OA is able to slide within a slot that is cut in link BC, as shown. Pins O and C are on the same horizontal line. At the instant shown, • link BC is vertical with L = 400 mm. • link OA is rotating in the CW sense at a rate of ωBC = 8 rad/sec.
y B
At the instant shown, find: a) the angular velocity of link BC. Write your answer as a vector.
A
b) the value for L! . HINT: In relating the velocities of A and C, use an observer attached to link BC. Also, let the xyz axes be attached to link BC.
500 mm
L
Link OA:
ωOA
v A = vO + ! OA "!r A/O
(
= 0 + (! OA k ) "! 0.3i + 0.4 j
)
x
= #0.4 ! OA i + 0.3! OA j Also,
O
v A = vC + ( v A/C )rel + ! "!r A/C
(
= 0 + L! j + (! BC k ) "! 0.4 j
)
= #0.4 ! BC i + L! j Equating and balancing coefficients:
! 0.4 " OA = !0.4 " BC j : 0.3" OA = L!
i:
# #
" BC = ( !8 k ) rad / sec L! = ( 0.3) ( !8 ) = !2.4 m / sec
C
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